Combine the chicken, pesto, and salt in a large bowl and mix just until combined; avoid overmixing. Pinch a teaspoon-size amount between your ngers and roll it into a ball; repeat to make 20 meatballs.
Heat the oil in a large skillet over medium-high heat. Add the meatballs in a single layer and cook until browned on the bottoms, about 2 minutes. Turn them over and cook until the opposite sides are browned and the meatballs are cooked through, 2 to 3 minutes more.
Transfer the meatballs to a paper towel–lined plate to drain.